A student investigates several aqueous reactions at 298 K. For each reaction the student determines the standard Gibbs free energy change, ΔG∘ (in kJ mol−1), as well as the corresponding equilibrium constant, K. The student plots ΔG∘ on the vertical axis versus lnK on the horizontal axis and obtains a straight line that passes through the origin with a measured slope of −2.48kJ.
(a) Identify the physical quantity represented by the magnitude of the slope and include the appropriate units in your answer.
(b) Give a theoretical explanation for why the straight-line plot is expected to pass through the origin in the absence of experimental error.
(c) Using this graph, describe the relationship between the sign of ΔG∘ and the magnitude of K for the set of reactions studied. Explain your reasoning in terms of the plotted variables.